Title: Properties of log canonical singularities in positive characteristic.Abstract: We will investigate if some well known properties of log canonical singularities over the complex numbers still hold true over perfect fields of positive characteristic and over excellent rings with perfect residue fields. We will discuss both pathological behavior in characteristic p as well as some positive results […]
Title: A Hodge-theoretic proof of Hwang's theoremAbstract: I will explain a Hodge-theoretic proof for Hwang's theorem, which says that if the base of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is smooth, then it must be projective space. The result is contained in a joint paper with Ben Bakker from last fall.
Title: Syzygies of adjoint linear series on projective varietiesAbstract: Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. Starting with the pioneering work of Mark Green on curves, numerous attempts have been made to extend these results to higher dimensions. Ein and Lazarsfeld proved that if A is a very ample […]
Title: Cohomological splitting of fibrations over rationally connected basesAbstract: A classical result of Blanchard and Deligne asserts that the rational cohomology of a smooth projective fibration splits additively. In this talk, I will discuss how to prove an analogous result for cohomology with coefficients in fields of positive characteristics. Although the splitting in this setting does not […]
Title: Curves on Varieties and the Degree of Irrationality.Abstract: Inspired by the Noether-Lefschetz theorem, it has been conjectured that the degree of any curve on a (very) general complete intersection variety is divisible by the degree of the variety itself. In this talk, we present a weaker version of this conjecture. Using this result, we confirm a […]
Title: Twisted Intermediate Jacobian Fibrations.Abstract:In this talk, I will report on a joint work in progress with D. Mattei and E. Shinder, where we construct, using Hodge modules, a group scheme that can be thought of as the intermediate Jacobian of a certain complete family of cubic threefolds. We show that the group scheme acts on […]
Title: Minimal Exponent of Local Complete Intersection Subvarieties.Abstract: Classification of singularities is an interesting problem in many areas of algebraic geometry, like the minimal model program. One classical approach is to assign to a singular subvariety a rational number, its log canonical threshold. For complex hypersurface singularities, this invariant has been refined by M. Saito to the […]
Title: Asymptotic Enumerativity of Tevelev Degrees.Abstract: A Tevelev degree is a type of Gromov-Witten invariant where the domain curve is fixed in the moduli. After reviewing the basic definitions and previously known results, I will report on joint work with Lehmann, Lian, Riedl, Starr, and Tanimoto, where we improve the Lian-Pandharipande bound on asymptotic enumerativity of Tevelev […]
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Title: Linear Chern-Hopf-Thurston conjectureAbstract: The Chern-Hopf-Thurston conjecture asserts that for a closed, aspherical manifold X of dimension 2d, the Euler characteristics satisfies $(-1)^dchi(X)geq 0$. In this talk, we present a proof of the conjecture for projective manifolds whose fundamental groups admit an almost faithful linear representation. Moreover, we establish a stronger result: all perverse sheaves on X […]
Title: Reconstructing schemes from their étale topoi.Abstract: In Grothendieck’s 1983 letter to Faltings that initiated the study of anabelian geometry, he conjectured that a large class of schemes can be reconstructed from their étale topoi. In this talk, I’ll discuss joint work with Magnus Carlson and Sebastian Wolf that proves Grothendieck’s conjecture for infinite fields. Specifically, we […]
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